What does it mean to say that "the population mean is a single fixed number?" I am trying to figure out what it means if a population mean value is fixed.
 A: Consider a finite population of values -- let's say you have a billion of them
The mean of that population is a single value -- you can compute it. If you recalculate it again on the same population, you use all the same values in your mean, so it's the same number every time.
By contrast if you take new samples the sample mean is different from one sample to the next, because the samples contain different individuals.
A: Here's how it finally made sense to me.
When we say something like, "human male height is normally distributed", we really mean it.  We actually believe that, whoever is in charge of this thing, has a book, and on a page of that book is written something like:

Human males.  Distributed like $N(70, 5)$, in units of inches.

When whoever is in charge needs a new male, they fire up their random number generator

Ok, I need a new male.  (Generates sample point), ok, 72 inches.

We don't get to see the book, we just get to see a bunch of males.  So the best we can do is use this bunch of males to attempt to infer what is in the book.
What is in the book is the population parameter.  What we get by using statistics and data is a parameter estimate.
